It's a bad life, but it is life and having an eternal life. The bible says the unsaved will not have life after judgment day so I will go with that.
John_3:36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life ; but the wrath of God abideth on him.
"shall not see life" means will not be alive.
This above is the reason for your error!
Life and death are both states of existence determined by an individuals state of being with God. The believer in Christ will have eternal life, which is eternal existence in the Joy of the Lord in the kingdom of God. The reference that the unbeliever "shall not see life" is the opposite of life, which means that the the individual will exist eternally in separation from God and condemned in the lake of fire.
You err because you interpret death as meaning to cease to exist. The truth is that life and death are two states of conscious existence.
Life = eternal conscious existence in the presence of the Lord in the kingdom of God
Death = eternal conscious existence in separation from God in the lake of fire
If Death meant that the individual ceases to exist, then they would have ceased to exist after the first death. Yet, there is a second death which is the lake of fire. How can they die once only to die a second time? As revealed in Revelation 20:11-15, the spirits of the unrighteous dead will be released from Hades receiving resurrected bodies and will stand before God at the GWTJ and will then be cast into the lake of fire where the they will endure their torment in those resurrected bodies.